NATIONAL AVIATION UNIVERSITY
Institute of Economics and Management
Management and Logistics Faculty
Management of Foreign Economic Activity of Enterprises Department
AGREED
Director of the Institute of
Economics and Management
APPROVED
Deputy Rector for Academics
_______________V. Matveev
“____”_______________2014
_____________ A. Polukhin
“___”______________2014
Quality Management System
COURSE TRAINING PROGRAM
on
Mathematic Statistics
(according to ECTS)
Major:
Specialty:
6.030601 “Management”
8.03060104 “Management of Foreign Economic Activity”
Year of Study – 5
Semester – 10th
Practicals
– 40
Self-study
– 50
Total (hours/ECTS credits) –90/2.5
Homework (1)
– 10th semester
Graded Test – 10th semester
Index Р6-8.03060104-а/14-4.2.3
QMS NAU CTP 11.02.03-01-2014
Quality Management System
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Mathematic Statistics
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The Course Training Program is based on the “Mathematic Statistics” Syllabus
with index Н7-8.03060101/14-4.2.3, approved __.__.2014; Master Extended
Curriculum № PМ-6-8.03060104-а/14 for Major 6.030601 “Management” by the
specialty 8.03060104 “Management of Foreign Economic Activity”; “The Temporal
Manual on organization of the educational training process on module principle
(experiment)” and “The Temporal Manual on the Rating System of knowledge
assessment” approved by the Rector of the University (order № 122/од of 15.06.2004,
order №81/од of 12.04.2005).
The Course Training Program has been developed by
professor of
the Management of Foreign Economic
Activity of Enterprises Department
__________V. Rodchenko
junior lecturer of
the Management of Foreign Economic
Activity of Enterprises Department
__________O. Rodchenko
Discussed and approved by the Department for Major 6.030601 “Management”
(Specialty 8.03060104 “Management of Foreign Economic Activity”) – Management
of Foreign Economic Activity of Enterprises Department, Record № 13 of 17/02/2014.
Head of the Department __________________________________ V. Novak
Discussed and approved by the Scientific-Methodological-Editorial Board of
the Institute of Economics and Management, Record №___ of "___" _______ 2014.
Head of the SMEB
____________________________ O. Borysenko
Director of the Institute
of Advanced Technologies
Document level – 3b
The planned term between the revisions – 1 year
Master copy
___________ M. Sidorov
Quality Management System
Course Training Program
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Mathematic Statistics
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CONTENTS
Introduction ……………………………………………..…………………...... 4
1. Explanatory notes………………………………………..…………………. 4
1.1. Subject status in the system of professional training………………………
4
1.2. Target of the subject………………………………………………………... 4
1.3. Objectives to study the subject…………………………………………….. 4
1.4. Integrated requirements for knowledge and skills of the subject (educational
module)…….……………………………………………………………………. 4
1.5. Interdisciplinary links of the subject……………………………………….. 5
2. Subject content……………………………………………………………… 5
2.1. Training schedule of the subject……………………………………………. 5
2.2. Development of the didactic process for different types of classes………… 6
2.2.1. Practicals, their subject matters and planned hours……………………… 6
2.2.2. Student self-study, its content and planned hours………………………..
6
2.2.2.1. Homework...……………………………………………………………. 7
3. Basic concepts of guidance on the subject………………………………… 7
3.1. List of references…………………………………………………………… 7
3.2. List of basic guidance materials for the subject……………………………
8
4. Rating System of knowledge and skills assessment………………………. 8
4.1. Basic terms and definitions…………………………………………………. 8
4.2. Methods of the knowledge and skills assessment rating system…………… 9
5. The forms of Quality Management System documents…………………..
12
Quality Management System
Course Training Program
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Mathematic Statistics
Document
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Independent thoughts arise only from selfacquired knowledge.
K.D. Ushinsky
INTRODUCTION
Detailed course training program of the subject is a must for successful educational process
according to the European Credit Transfer System. Teachers and students are to be familiarized
with it.
Grading system of assessment (GSA) is an integral part of the work course training program
providing assessment the quality of all kinds of auditorium educational work and self-study
performed by a student, as well as acquired knowledge and skills through grading assessment of
results of this work in the current, modular and semester control with transfer of the grades by
multi-grade scale to the national grading scale and ECTS scale.
1. EXPLANATORY NOTES
1.1. Subject status in the system of professional training
Course training program on the subject «Mathematic Statistics» reflects the essence of
the methodology, concepts, methods and techniques in statistics.
1.2. Target of the subject
The goal of teaching the subject is to introduce with the methods of statistics, develop
abilities for applying in practice on the enterprise or organization.
1.3. Objectives to study the subject
The tasks of mastering the subject are the following:
- familiarizing students with the process of statistical estimation;
- familiarizing students with the process of statistical verification;
- developing skills of practical problem-solving in the area of organization management
with use of tools and methods of mathematical statistics.
1.4. Integrated requirements for knowledge and skills of the subject (educational module)
As a result of mastering the subject a student shall:
Know:
- appropriate methods of mathematical statistics;
- one- and two-dimension distribution of random variable;
- function of probability;
- probability density function;
- cumulative distribution function of a discrete and continuous random variable;
- parameters of distribution of random variable;
- differential and integral calculus.
Learning outcomes:
- to solve management problems using methods of mathematical statistics;
- select and apply statistical estimation and verification procedures and interpret the
results;
- analyze and compile statistical data on the given problem, analyze and interpret them
properly, draw conclusions and make appropriate recommendations;
- effectively present completed task;
- apply an analytical approach to organization management problems.
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1.5. Interdisciplinary links of the subject
Information Systems and
Technologies in the
Management of Foreign
Economic Activity
Strategic
Management of
Corporations
Modern
Management
Conceptions
International
Logistics
Mathematic
Statistics
Process Management
Methodology and
Organization of
Scientific
Researches
International
Management and
Marketing
Investment
Management
Management of Foreign
Economic Activity
2. SUBJECT CONTENT
2.1. Training schedule of the subject
№
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Academic Hours
Topic
All
Lectures
10th Semester
Module №1 "Mathematic Statistics"
Fundamental ideas of statistics, descriptive
6
and mathematical statistics
Сalculus of probability distribution of
28
random variable
Estimation of unknown parameters of
12
general population
Statistical hypotheses, testing statistical 12
hypothesis,
parametrical
and
nonparametrical hypothesis
Analysis of multidimensional phenomena,
20
correlation dependency analysis
Module Test
4
Homework
8
Total for the module №1
90
th
Total for 10 semester
90
Total for the subject
90
-
Practicals
Selfstudy
2
4
14
14
6
6
6
6
10
10
2
40
40
40
2
8
50
50
50
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2.2. Development of the didactic process for different types of classes
2.2.1. Practicals, their subject matters and planned hours
№
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
Topic
2
10th Semester
Module №1 "Mathematic Statistics"
Methods of mathematical statistics
Discrete random variables and probability distributions
Continuous random variables and probability distributions
Bivariate discrete and continuous random variables
Discrete bivariate distributions
Continuous bivariate distributions
Distribution functions, probability densities, and their relationship
The cumulative distribution function of a discrete and of a
continuous random variable
Distributions associated with the normal population
Techniques for finding point estimators of parameters
Techniques for finding interval estimators of parameters
Hypotheses and test procedures
Tests about a population mean
Tests concerning a population proportion. P-Values
The simple linear and logistic regression models
Estimating model parameters
Correlation
Multiple regression analysis
Regression with matrices
Module Test
Total for the module №1
Total for 10th semester
Total for the subject
Academic Hours
SelfPracticals
study
3
4
2
2
2
2
2
2
2
2
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
40
40
40
2
2
2
2
2
2
2
2
2
2
2
2
42
42
42
2.2.2. Student self-study, its content and planned hours
№
Self-study Content
1
2
10th Semester
1. Preparation to practicals
2. Preparation to Module Test
3. Carrying out of Homework
Total for the subject
Academic
Hours
3
40
2
8
50
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2.2.2.1. Homework
Homework is carried out in the tenth semester according to the approved methodical guide
for fastening and deepening of theoretical knowledge and skills received by the student in the
course of subject material in area of mathematic statistics.
For successful homework carrying out student should know methods of mathematic
statistics; be able to select and apply statistical estimation and verification procedures and
interpret the results; analyze and compile statistical data on the given problem, analyze and
interpret them properly, draw conclusions and make appropriate recommendations; effectively
present completed task; apply an analytical approach to organization management problems.
Performance of homework is an important stage in preparing to perform master thesis in
management of the foreign economic activity.
Homework purpose is concretized according to a theme and problems of master thesis.
Performance, designing and protection of homework are carried out by the student
individually in accordance to methodological recommendations.
Time required for carrying out the homework is equal up to 8 academic hours of selfstudy.
3. BASIC CONCEPTS OF GUIDANCE ON THE SUBJECT
3.1. List of references
Basic literature
3.1.1. Вашків П.Г. та ін. Теорія статистики. – К.: Лебідь, 2001. – 320 с.
3.1.2. Статистика: підручник / С.С. Герасименко та ін. – 2-е вид., перероб і доп. –
К.: КНЕУ, 2000. – 467 с.
3.1.3. Ковтун Н.В., Столяров Г.С. Загальна теорія статистики: курс лекцій. – К.:
Четверта хвиля, 1996. – 144 с.
3.1.4.Грабовецький Б.Є. Загальна теорія статистики: навч. посіб. – Вінниця.: ВДТУ,
2001. – 147 с.
3.1.5.Єріна А.М., Кальян З.О. Теорія статистики: практикум. – К.: Т-во “Знання”,
КОО, 1997. – 325 с.
3.1.6. George G. Roussas A Course of Mathematical Statistics, Second Edition
[Електронний ресурс]. – California: Academic Press, 1997. – 593 p. – Режим доступу:
http://www.lce.esalq.usp.br/arquivos/aulas/2012/LCE5806/A_course_in_mathematical_statistics
_George_G._Roussas_p593.pdf
3.1.7. John I. Marden Mathematical Statistics. Old School [Електронний ресурс],
Department of Statistics, University of Illinois at Urbana-Champaign, 2012. – 271 p. – Режим
доступу: http://www.istics.net/pdfs/mathstat.pdf
3.1.8. Sara van de Geer Mathematical Statistics [Електронний ресурс], September 2010.
– 142 p. – Режим доступу: www.stat.math.ethz.ch/~geer/mathstat.pdf
Additional literature
3.1.9. Фещур Р. В., Барвінський А. Ф., Кічор В. П. Статистика. Теоретичні основи і
прикладні аспекти: навчальний посібник. – Львів: "Інтелект-Захід", 2001 – 276 с.
3.1.10. Вашків П.Г. та ін. Статистика підприємства: навч. посібник. – К.:
“Слобожанщина”, 1999. – 600 с.
3.1.11. Статистика: курс лекций / Харченко Л. П., Долженкова В. Г., Ионин В. Г. и
др.; под ред. В. Г. Ионина. – Новосибирск: Изд-во НГАЗ иУ, М.: ИНФРА-М, 1998. – 310 с.
3.1.12. Jay L. Devore, Kenneth N. Berk Modern Mathematical Statistics with
Applications [Електронний ресурс]. – California, Illinois: Thomson, 2007. – 849 p. – Режим
доступу: www.acc.umu.se/~marshi/Courses/...10/0534404731MathStatistB.pdf
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3.1.13. Prasanna Sahoo Probability and Mathematical Statistics [Електронний ресурс],
Department of Mathematics, University of Louisville, 2013. – 712 p. – Режим доступу:
erdos.math.louisville.edu/~pksaho01/teaching/Math662TB-09S.pdf
3.2. List of basic guidance materials for the subject
№
1.
2.
3.
Name
Slides, posters
Set of tests for module test
Methodical guide for carrying out
Homework
Index of Topics where
Guides are Used
1.1-1.8
1.9
1.10
Amount
2 copies and e-version
30 copies and e-version
e-version
4. RATING SYSTEM OF KNOWLEDGE AND SKILLS ASSESSMENT
4.1 Basic terms and definitions
4.1.1. Semester Examination is a form of final check of how well a student has mastered
both theoretical and practical material in a given subject during a semester. Written examination
is held during the examination period in the presence of a board of examiners headed by the head
of the department in accordance with the established time-table.
Semester control is performed at the University in written form or by using computer
technologies in order to provide objectivity and transparency of control of acquired knowledge
and skills of students. This provision does not apply to the courses, presentation of educational
material of which requires from the student mainly verbal responses. The list of subjects with
oral (combined) form semester control is set separately for each major (specialty) preparation of
specialists with the permission of Deputy Rector for Academics.
4.1.2. Semester Graded Test is a form of final check of how well a student has mastered
material in a given subject based on results of his performance of all kinds of academic activity
through the semester: audience work during lectures and practical classes and self-study during
performance of self-test assignments (homeworks performance, etc).
Semester Graded Test does not require student’s presence and is passed provided student
has done all previous kinds of academic activity specified by the Course Training Program of the
subject and has received positive in national scale total module grades for each module. Teacher
has right to run additional test, interview, express-test etc. to specify particular positions.
4.1.3. ECTS system is a model of academic process organization based on a combination
of two constituents: module technology of training and credits (Test Units) and covers the
content, forms and facilities of academic process, forms of checking students’ knowledge and
skills quality as well as academic activity of students both in class and outside it (i.e. self-study).
The ECTS system aims at making students work on a systematic basis during the semester in
view of their future professional success.
4.1.4. A module is a logically complete, relatively independent integral part of a training
course, a set of theoretical and practical tasks of relevant content and structure with an elaborated
system of methodical, educative, individual and technological support, a necessary component of
which is an appropriate form of grading.
4.1.5. A credit (test unit) is a single unit of measuring work done by students both in
class and outside it (Academic Load) which is equivalent to 36 working hours.
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4.1.6. A grade is a quantitative measuring unit of students’ learning outcomes
assessment, based on a multi-value scale as they perform their pre-assigned set of academic
tasks.
4.1.7. The ECTS grading system is a system of measuring the quality of all types of
classroom and self-study work done by students as well as the level of their knowledge and skills
by assessing them in values according to the 100-value scale with further transfer of these values
into the national scale and the ECTS system.
The grading system envisages the use of the following grades: the current module grade,
the module test grade, the total module grade, the semester module grade, the examination grade
and the total semester grade.
4.1.7.1. The current module grade consists of values which a student gets for a certain
kind of academic work in mastering a given module, i.e. doing and defending his/her individual
tasks at practical classes.
4.1.7.2. The module test grade is determined in values and in national scale grades as a
result of doing the module test.
4.1.7.3. The total module grade is determined in values and in national scale grades as
the sum of the current module grade and test module grade.
4.1.7.4. The semester module grade is determined in values and in national scale grades
as the sum of the total module grades obtained after studying the material of all the modules
within a semester.
4.1.7.5. The examination grade is determined (in values and in national scale) as the
results of the performance of the examination tasks.
4.1.7.6. The graded test grade is determined (in values and in national scale by the results
of all kinds of academic activity through the semester.
4.1.7.7. The total semester grade is determined as the sum of the semester module grade
and the examination grade (graded test grade in the case of graded test) in values, national scale
grades and ECTS system grades.
4.2. Methods of the knowledge and skills assessment rating system
4.2.1. Grading of different kinds of academic activities performed by a student and
obtained knowledge and skills are realized in values in line with Table 4.1.
Table 4.1
Grading of different kinds of academic activities performed by a student
10th Semester
Module №1
Мах
Grade
Carrying out individual task (10 values*4 classes)
40 (total)
Carrying out tests (5 values*2 classes)
10 (total)
Carrying out and defense of Homework
12
For carrying out module test № 1, a student must receive not less than 37 values
Module Test №1
26
Total for module №1
88
Semester Graded Test
Total Semester Grade
Kind of Academic Activities
Мах
Grade
12
100
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4.2.2. The completed curricular activity is accounted if the student received a positive mark
according to the national scale given in the Table 4.2 below.
Table 4.2
Correspondence between the Grades and the National Scale
Carrying out
individual tasks
9-10
8
6-7
under 6
Grades
Carrying out
Carrying out and
tests
defense of Homework
5
11-12
4
9-10
3
7-8
under 3
under 7
Module
Test
24-26
20-23
16-19
under 16
National Scale
Excellent
Good
Satisfactory
Bad
4.2.3. The grades a student has been given for the different kinds of academic work are
summed up and the result constituting a Current Module Grade is entered into the Module Grade
Register.
4.2.4. If a student has successfully done all kinds of academic work within the given
module and has got a positive Current Module Grade – not less than satisfactory according to the
national scale, he/she is allowed to take his/her module test.
4.2.5. Students have their Module Test in a written form. The procedure, which lasts up
to two academic hours, is held by a commission headed by the head of the department
responsible for the discipline.
4.2.6. The Current Module Grade and the Module Test Grade together make up the Total
Module Grade whose correspondence to the National Scale is shown in Table 4.3.
Table 4.3
Correspondence between the Total Module Grades and the National Scale
Module №1
79-88
66-78
53-65
under 53
National Scale
Excellent
Good
Satisfactory
Bad
4.2.7. A student is considered to have passed the module if both his/her Current Module
Grade and Module Test Grade are positive, i.e. higher than «bad» according to the national scale
(Tables 4.2), which yields a positive Total Module Grade (Table 4.3).
4.2.8. If a student has missed the module test due to any reason (being ill, debarred, etc.),
the entry «absent» is made against his/her name in the column «Module Test Grade» and the
entry «unclassified» – in the column «Total Module Grade».
The student is considered as not having an academic incomplete if he/she is allowed to
take his/her module test but has missed it due to a valid reason. Otherwise he/she is considered
as having an academic incomplete.
Further testing the student in this module is done in accordance with the established procedure.
4.2.9. In case if the student received a negative module test rating mark, they have a
chance to retake the test according to the established procedure.
4.2.10. In case of retaking the module test, the maximum module test point-based rating
mark equals twenty three («Good» mark according to the national scale), i.e. it is three points
less than that given in Table 4.2.
4.2.11. A student is not allowed to increase his/her positive Total Module Grade by
taking a repetitive test.
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4.2.12. The Semester Module Grade is calculated as the sum of the Total Module Grades. The
correspondence between Semester Module Grade values and the National Scale is given in Table 4.4.
Table 4.4
Correspondence between the Semester
Module Grades and the National Scale
Semester Grades
National Scale
79-88
66-78
53-65
under 53
Excellent
Good
Satisfactory
Bad
Table 4.5
Correspondence between the Graded
Test, Grades and the National Scale
Graded Test
Grades
12
10
8
-
National Scale
Excellent
Good
Satisfactory
-
4.2.13. The Semester Module Grade and the Graded Test Grade together make up a Total
Semester Grade whose correspondence to the National Scale and the ECTS System is shown in
Table 4.6.
Table 4.6
Correspondence of the Total Semester Grades to the National Scale
and the ECTS System
Total Semester
Grades
National
Scale
90-100
Excellent
82 – 89
75 – 81
B
Good
67 – 74
60 – 66
C
D
Satisfactory
35 – 59
1 – 34
ECTS System
ECTS
Grade
A
E
FX
Bad
F
Explanation
Excellent
(excellent performance with insignificant shortcomings)
Very Good
(performance above the average standard with few mistakes)
Good
(good performance altogether with a certain number of
significant mistakes)
Satisfactory
(performance meets the average standards)
Sufficient
(performance meets the minimal criteria)
Bad
(bad performance; a second testing is required)
Bad
(very bad performance; a student shall retake the course)
4.2.14. Total Semester Grade, in the Graded Test Semester (for this subject – in the 10th
Semester), equals the sum of Semester Module Grade and the minimal Graded Test Grade
established for each category of Semester Module Grades (12 for «Excellent», 10 for «Good»,
and 8 for «Satisfactory») that recalculates to the National Scale and the ECTS Scale.
4.2.15. A student is not allowed to increase his/her positive Total Semester Grade by
taking a repetitive Graded Test.
4.2.16. The Total Semester Grades, National Scale grades and ECTS System grades is
entered into the Examination Register and into a student’s record book.
4.2.17. The Total Semester Grade is entered into the Examination Register and into a
student’s record book in values, National Scale grades, and ECTS Scale grades, for example:
92/Ex/А, 87/Good/В, 79/Good/С, 68/Sat/D, 65/Sat/Е, etc.
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(Ф 03.02 – 01)
АРКУШ ПОШИРЕННЯ ДОКУМЕНТА
№
прим.
Куди
передано
(підрозділ)
Дата
видачі
П.І.Б. отримувача
Підпис
отримувача
Примітки
(Ф 03.02 – 02)
АРКУШ ОЗНАЙОМЛЕННЯ З ДОКУМЕНТОМ
№
пор.
Прізвище ім'я по-батькові
Підпис
ознайомленої
особи
Дата
ознайомлення
Примітки
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(Ф 03.02 – 04)
АРКУШ РЕЄСТРАЦІЇ РЕВІЗІЇ
№
пор.
Прізвище ім'я по-батькові
Дата ревізії
Висновок щодо
адекватності
Підпис
(Ф 03.02 – 03)
АРКУШ ОБЛІКУ ЗМІН
№
зміни
№ листа (сторінки)
Зміненого Заміненого
Нового
Анульованого
Підпис
особи,
яка
внесла
зміну
Дата
внесення
зміни
Дата
введення
зміни
(Ф 03.02 – 32)
УЗГОДЖЕННЯ ЗМІН
Підпис
Розробник
Узгоджено
Узгоджено
Узгоджено
Ініціали, прізвище
Посада
Дата